Questions tagged [cointegration]

Cointegration is often used in statistical abitrage as a way to identify how to combine some tradable instrument to obtain a *mean reverting* one.

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62 views

Pairs Trading: Normalized price series (co-integrated and correlated) always end up diverging

Need some expert advice and suggestions: I am trying out pairs trading or statistical arbitrage (as traders say). But even if two price series are co-integrated (ADF test, Hurst exponent, Ornstein–...
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What is the logic of the eigenvectors of the Johanson cointegration test determining hedge ratios?

Reading Algorithmic Trading: Winning Strategies and Their Rationale, Ernie Chan and there is a short section about the Johanson test for cointegration where it is mentioned that the eigenvectors ...
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Why is OLS based spread not reflective of actual difference?

I'm trying to define and track the spread between two time series (data available here), for the purpose of learning pair trading basics. When running a cointegration test the two series seem to be ...
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When constructing a cointegrating series, does choosing the linear regression with the lowest ADF test statistic yield the optimal hedging ratio?

Multiple sources say that you should find the optimal hedging ratio between two stocks in a pairs trade by conducting 2 linear regressions (with each stock as the independent variable), and using ...
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Cointegration and Ratio Pair Trading

I'm having some confusion doing Engle-Granger Cointegration test and then trade the ratio. Methodology: Run an OLS fit for A and B price time series without a constant. Therefore, $\hat{Y} = \gamma \...
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lead lag relationship among futures, options and stock prices

I have the data of past 10 years of NIFTY (the National Stock Exchange of India) stock, futures and options and I want to show the lead-lag relationship (which reacts first, futures, options or stocks)...
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Understanding output from Johansen Cointegration test

I have a VECM model that Im using to determine the revenues for a firm, based on factors like Interest rates, S&P 500 and company specific variables, as follows: Stage 1: $$z_t= a+ bX_t+e_t$$ ...
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Engle-Granger Regression for returns or prices?

Im trying to find a cointegration relationship between a spot and futures series as I'd like to compute the optimal hedge ratios. As I find the spot and futures at the price level to be nonstationary, ...
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What value to put in lm() function when testing for cointegration (R)

I'm a CS student working on a financial computing project + have a question regarding cointegration testing using linear regression with the lm() function. https://www.rdocumentation.org/packages/...
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Johansen cointegration Test for spread generation

I'm using the python statsmodels version of the johansen cointegration test and I'm looking for some advice on how best to generate the spread used within a pairs trading algorithm. For example I've ...
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Law of one Price and Cointegration relationship

I have a question on the relationship between the law of one price and cointegration of (financial) time series. To set things clear I start with something simple: Suppose there is an unobserved "...
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What does the cointegration coefficient represent in pairs trading when cointegrating log stock prices?

In Pairs Trading by Vidyamurthy, on page 83 (and throughout the book), the author describes an elementary example of trading with log prices. The long run equilibrium of the basic portfolio is given ...
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Cointegration between prices and dividends. How do I get the following expression?

Actually, I have two questions: 1. Let us assume that expected returns are constant. Then, we have the following expression for how the prices should be determined, provided that the operators are ...
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Trading 3 stocks X Y Z where X cointegrated to Y, Y to Z, but no other cointegration is available

Suppose you have 3 stocks, say X Y Z. You also know that X is cointegrated to Y using some test (say ADF) and Y is cointegrated to Z. However, no transitivity, and no threesome cointegration ...
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generalisation of cointegrated stock pair strategies to multiple cointegration

Question: as it is well known, there are strategies to trade pairs of stocks which are known to be co-integrated. See for instance here: https://medium.com/auquan/pairs-trading-data-science-...
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when a co-integrated times series pair has broken the leash

I have two times series, say $T_i$ and $S_i$ over a reasonably large time window, and I have calculated their cointegration (using python's OLS and Adfuller) . Say that the test has passed with high ...
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Spot trading: exact mathematical definition of the positions for a portfolio

Let us say that I want to spot trade a portfolio constituted of a pair of two stocks of respective prices (for example in USD) $S^1_t$ and $S^2_t$, and suppose for example that they co-integrate ...
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Fractional cointegration in R

I'm looking for a package (or some code that anyone has written) that will help me to estimate a VECM for fractionally cointegrated series. I.e. like the ca.jo ...
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Pairs trading strategy: Portfolio returns and NAV

Currently trying a pairs trading approach using cointegration. Tried both formations: $$log(P_t^A)=log(P_t^B) \hat{\gamma}+\hat{\mu}+\epsilon_t \hspace{0.5cm} (1)$$ $$P_t^A=P_t^B \hat{\gamma}+\hat{\...
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Johansen Cointegration Test in R

I know its probably been asked bevor but i just don't get it. I have 2 values (Oil and corn price) and i want to check if they are cointegrated. Bevor that, i have tested if they really are non ...
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Need help on cointegration

I tried to test stock pairs for pairs trading. There are two questions I am not sure. I am not using ADF to test the log difference between two stocks. But I also see people using Johansen test. What'...
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Cointegration between daily time series and intraday time series

I am working with time series data of daily prices, and intraday prices. For simplicity sake I will refer to the daily time series as 'A' and 'B', and the intraday time series of the same instruments ...
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Is my coding for my kalman filter off when testing this specific set of pairs?

My kalman filter seems to be off for this specific set of pairs I'm looking at. As you can see, in the kalman filtered linear regression, there seems to be an outlying blue line nowhere near the data ...
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Does Chan use the wrong state transition model in his Kalman filter code?

In his book, Algorithmic Trading: Winning Strategies and Their Rationale, Ernie Chan shows how to use a Kalman filter to improve the returns of a cointegrated portfolio. Recall that the state equation ...
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243 views

Cointegration on prices or difference of prices

Is it better to run my cointegration tests on prices or difference of prices? Difference of prices are more likely to be stationary so the results of my regression (which gives me the beta for my ...
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Minimizing variance when searching for Cointegration

This paper by Meucci explains that in order to find a combination leading to cointegration of several series $X$, you have to find the vector $w$ which minimise the quantity $\textrm{Var}(w'X)$. I do ...
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cointegration applied to Portfolio Construction & Risk management

There are all sorts of applications of cointegration to generating alpha on mean-reverting timeseries: comparing spot vs. futures, bond spreads, identifying mean-reverting residuals, etc. But there ...
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Imposing Restrictions on Cointegrating Vectors, R example

The code given below estimates a VEC model with 4 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor). ...
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How do different methods and techniques used in pairs trading compare?

I was going through the paper of Avellaneda (2008) on stat arb and I found it interesting that he uses asset returns vs. their respective ETFs to compute the s-score. I am wondering if anyone has ...
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How to determine ratios for mean-reverting basket

Suppose I have a basket of 3 securities A, B, and C. I believe that the basket is cointegrated and I want to create a mean-reverting trade. I fit the model: $\log(A)=\beta_b*\log(B)+\beta_c*\log(C)+\...
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Are two identical time series cointegrated?

I did cointegration test on two identical time series, and the result shows that they are not cointegrated, but intuitively, I think they are. Can anyone share some thoughts on this? Thanks!
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Are there any papers about cointegration consisting of time series of more than two assets?

Are there any papers about cointegration consisting of time series of more than two assets ? I wonder if there could be any trading strategy for three assets case.
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pair trading cointegration - calculating shares quantities traded, portfolio value and returns

I have a trading strategy based on the cointegration of X and Y where beta derived from the regression is 0.7. My initial capital to invest is 1000. My understanding that the quantities of X and Y to ...
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Cointegration vs combination of returns

Hi Quantitative Finance, I understand that there are a wealth of pairs trading models out there. Recently, it got me thinking as to why we go through the trouble to find cointegrated pairs while we ...
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Johansen Cointegration Test

I just performed a Johansen Co-integration test on two stocks. The results I get are: ans = r0 r1 t1 true false I am using Matlab. Can ...
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Cointegration and pairs trading

I have intuition that cointegration between elements of pair of equities somehow contradicts pairs trading strategies. Because the better is linear fit of the model the less opportunities we have for ...
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Spurious regression between two futures with the same underlying highly correlated (cor=0.9)

analyzing the correlation between soybean and soybean meal futures in ECBOT, and making a linear regression in R between them I check with an ADF Test that the residuals are not stationary, so ...
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Cointegration results interpretation validation?

Here is how I am interpreting results of a Johansen Cointegration Test and Engel-Granger Test for A and B. The results:(Using matlab) ...
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Looking for materials regarding Pair Trading [closed]

For my master thesis, I wish to work onto Cointegration and Pair Trading. I was wondering if any of you had some scholar/blog material recommendations. Best Regards
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Why does the presence of cointegration solve the problem of spurious correlation? [closed]

Many of us are familiar with the connection between spurious correlation and its relationship to cointegration. Granger explains in his seminal 1974 paper "Spurious Regressions in Econometrics" how ...
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How do you decide what time frame you're going to use when testing for cointegration?

I've been fiddling around with different time frames when doing tests for cointegration between two timeseries, and I've realized that the dates that you use for your start/stop of the test will ...
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Johansen test on two stocks (for pairs trading) yielding annoying results

I hope you can help me with this one. I am using cointegration to discover potential pairs trading opportunities within stocks and more precisely I am utilizing the Johansen trace test for only two ...
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Cointegration pair trading - how to test a trading rule using Monte Carlo?

I am doing a research exercise where I have two price series $X_t, Y_t$ which I regress against each other and test for cointegration. Once I confirm that they are cointegrated (using CADF or ...
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Does cointegration contradict the market efficiency?

It is generally assumed that market prices follow random walks, implying market efficiency. However, one could find that some combinations of the "random walks" are cointegrated. Does this ...
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Simulating Co-Integrated Assets

I know how to simulate correlated returns, but I do not know how to simulate Co-Integrated assets. I would like to simulate a co-integrated time series where the Beta Co-Efficient is not constant, but ...
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cointegration strategy

If it can be proved that two time series $$S_t^1=\alpha + \beta S_t^2 + \xi_t$$ representing stocks are correlated, with $\beta=-2$ and then are proved to be cointegrated, how a portfolio should be ...
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Co integration of diverging time series

I have 2 time-series datasets. I am trying to find co integration between them. Now the thing is they are negatively correlated. So if I want to look at the distance between them, would I be right in ...
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How do I test if my betas form a co-integrated vector?

I have identified a model using principal component regression where $Y_t$ is explained by 4 factors such as: $$Y_t = \beta_1 X_{1t} + \beta_2 X_{2t} + \beta_3 X_{3t} + \beta_4 X_{4t} + \epsilon_t$$ ...
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how to mix trading signals for the same product?

I have multiple trading signals developed using cointegration on the same stock using various correlated assets. Is there a mathematical way to combine them to achieve better entry/exit points and ...